Designing efficient car parking mechanisms that can be potentially integrated into future intelligent transportation systems is of crucial importance. Usually, the related design problems are combinatorial and the worst-case complexity of optimal solution approaches grows exponentially with the problem sizes. Therefore, such optimal approaches are not scalable and practically undesirable. As a result, almost all existing methods for parking slot assignment are simple and greedy approaches, where each car is assigned a free parking slot, which is closer to its destination. Moreover, no emphasis is placed to optimize the social benefit of the users during the parking slot assignment. In this paper, the fairness as a metric for modeling the aggregate social benefit of the users is considered and a distributed algorithm based on Lagrange duality theory is developed. The proposed algorithm is gracefully scalable compared to the optimal methods. In addition, it is shown that the proposed car parking mechanism preserves privacy in the sense that any car involved in the algorithm will not be able to discover the destination of any other car during the algorithm iterations. Numerical results illustrate the performance of the proposed algorithm compared to the optimal assignment and a greedy method. They show that our algorithm yields a good tradeoff between the implementation-level simplicity and the performance. Even though the main emphasis in this paper resides in the car parking slot assignment problem, our formulation and the algorithms, in general, can also be applied or adopted in fair agent-target assignment problems in other application domains.